Phase-shift interferometry is an established method for measuring a variety of physical parameters ranging from intrinsic properties of gases to the displacement of objects such as described in a review article by J. Schwider entitled “Advanced Evaluation Techniques In Interferometry,” Progress In Optics XXVIII, Ed. E. Wolf (Elsevier Science Publishers 1990). The contents of the Schwider article are herein incorporated in their entirety by reference. Interferometric wavefront sensors can employ phase-shift interferometers (PSI) to measure the spatial distribution of a relative phase across an area or two-dimensional section, i.e., to measure a physical parameter across a two-dimensional section.
An interferometric wavefront sensor employing a PSI typically consists of a spatially coherent light source that is split into two beams, a reference beam and a measurement beam, which are later recombined after traveling respective optical paths of different lengths. The relative phase difference between the wavefronts of the two beams is manifested as a two-dimensional intensity pattern or interference signal known as an interferogram. PSIs typically have an element in the path of the reference beam which introduces three or more known phase-shifts. By detecting the intensity pattern with a detector for each of the phase-shifts, the relative phase difference distribution of the reference and measurement beam wavefronts can be quantitatively determined independent of any attenuation in either of the reference or measurement beams.
Phase shifting in homodyne detection methods using phase shifting methods such as piezo-electric driven mirrors have been widely used to obtain high-quality measurements under otherwise static conditions. The measurement of transient or high-speed events have required in prior art either ultra high speed phase shifting, i.e., much faster than the event time scales and corresponding detector read out speeds, or phase shifting apparatus and methods that can be used to acquire the required information by the essentially instantaneous measurements.
Effects of atmospheric turbulence in the reference and measurement paths of a wavefront interferometer reduce fringe contrast and introduce statistical errors in a measured wavefront profile. The essentially instantaneous measurements are used in prior art to reduce the effects of atmospheric turbulence on fringe contrast. However, the technique of the essentially instantaneous measurements of prior art does not reduce the magnitude of the statistical errors. Accordingly, the statistical effects of atmospheric turbulence in wavefront interferometry based on the technique of the essentially instantaneous measurements of prior art are subsequently reduced in the prior art by averaging a number of statistically independent the essentially instantaneous measurements of a wavefront profile.
Several methods of spatial phase shifting have been disclosed in the prior art which are directed to the acquisition of the essentially simultaneous measurements of electrical interference signal values. In 1983 Smythe and Moore described a spatial phase-shifting method in which a series of conventional beam-splitters and polarization optics are used to produce three or four phase-shifted images onto as many cameras for simultaneous detection. A number of US patents such as U.S. Pat. Nos. 4,575,248, 5,589,938, 5,663,793, 5,777,741, and 5,883,717 disclose variations of the Smythe and Moore method where multiple cameras are used to detect multiple interferograms.
One of the disadvantages of these methods is that multiple cameras are required or a single camera recording multiple images and complicated optical arrangements are required to produce the phase-shifted images. The disadvantages and limitations of using multiple cameras or a camera recording multiple images are described and addressed for example in the commonly owned U.S. Provisional Patent Application No. 60/442,858 and U.S. patent application Ser. No. 10/765,368 wherein both are entitled “Apparatus and Method for Joint Measurements of Conjugated Quadratures of Fields of Reflected/Scattered and Transmitted Beams by an Object in Interferometry.” Both U.S. Provisional Patent Application No. 60/442,858 and U.S. patent application Ser. No. 10/765,368 are by Henry A. Hill and the contents of each of which are herein incorporated in their entirety by reference.
An alternative technique for the generation of four simultaneous phase-shifted images for a homodyne detection method has also been disclosed by J. E. Millerd and N. J. Brock in U.S. Pat. No. 6,304,330 B1 entitled “Methods And Apparatus For Splitting, Imaging, And Measuring Wavefronts In Interferometry.” The technique disclosed in U.S. Pat. No. 6,304,330 B1 uses holographic techniques for the splitting of a beam into four beams. The four beams are detected by a single multi-pixel detector. One consequence of the use of a single multi-pixel detector to record four phase-shifted images simultaneously is a reduction in frame rate for the detector by a factor of approximately four compared to a PSI recording a single phase-shifted image on a single multi-pixel detector with the same image resolution. It is further observed that since the generation of the multiple beams in the technique described in U.S. Pat. No. 6,304,303 B1 is performed on a non-mixed beam of an interferometer, the alternative technique of U.S. Pat. No. 6,304,303 B1 is most readily applicable to for example a Twyman-Green type interferometer.
Another alternative technique for generating the equivalent of multiple simultaneous phase shifted images has also been accomplished by using a tilted reference wave to induce a spatial carrier frequency to a pattern in an interferogram, an example of which is disclosed by H. Steinbichler and J. Gutjahr in U.S. Pat. No. 5,155,363 entitled “Method For Direct Phase Measurement Of Radiation, Particularly Light Radiation, And Apparatus For Performing The Method.” This another alternative technique for generating the equivalent of multiple simultaneous phase shifted images requires the relative phase of the reference and measurement field to vary slowly with respect to the detector pixel spacing.
The another alternative technique for generating the equivalent of multiple simultaneous phase shifted images using a tilted reference wave is also used in an acquisition technology product FlashPhase™ of Zygo Corporation. The steps performed in FlashPhase™ are first acquire a single frame of intensity or interferogram, next generate a two-dimensional complex spatial frequency map by a two-dimensional finite Fourier transform (FFT), next generate a filter and use the filter to isolate a first order signal, then invert the filtered spatial frequency map by an inverse two-dimensional FFT to a phase map or wavefront map. Although the acquisition technology product FlashPhase™ is computationally complex, it is very fast on today's powerful computers.
A difficult procedure related to the refractive index of a gas is the compensation of refractive index fluctuations over reference and measurement paths of unknown or variable length and with uncontrolled temperature and pressure. Example situations are in Fizeau and Twyman-Green interferometers and high-precision linear displacement interferometry such as is employed in manufacturing of optical elements and in micro-lithographic fabrication of ICs. See for example an article entitled “Residual Errors In Laser Interferometry From Air Turbulence And Nonlinearity,” by N. Bobroff, Appl. Opt. 26(13), 2676-2682 (1987) and an article entitled “Recent Advances In Displacement Measuring Interferometry,” also by N. Bobroff, Measurement Science & Tech. 4(9), 907-926 (1993).
As noted in the aforementioned cited references, interferometric displacement measurements in a gas are subject to environmental uncertainties, particularly to changes in air pressure and temperature; to uncertainties in air composition such as resulting from changes in humidity; and to the effects of turbulence in the gas. Such factors alter the wavelength of the light used to measure the displacement. Under normal conditions the refractive index of air for example is approximately 1.0003 with a variation of the order of 1×10−5 to 1×10−4. In many applications the refractive index of air must be known with a relative precision of less than 0.1 ppm (parts per million) to less than 0.001 ppm, these two relative precisions corresponding to a displacement measurement accuracy of 100 nm and less than 1 nm, respectively, for a one meter interferometric displacement measurement.
There are frequent references in the art to heterodyne methods of phase estimation, in which the phase varies with time in a controlled way. For example, in a known form of prior-art heterodyne distance-measuring interferometer, the source emits two orthogonally polarized beams having slightly different optical frequencies (e.g. 2 MHz). The interferometric receiver in this case is typically comprised of a linear polarizer and a photodetector to measure a time-varying interference signal. The signal oscillates at the beat frequency and the phase of the signal corresponds to the relative phase difference. A further representative example of the prior art in heterodyne distance-measuring interferometry is taught in U.S. Pat. No. 4,688,940 issued to G. E. Sommargren and M. Schaham (1987). These known forms of interferometric metrology do not compensate for fluctuations in refractive index of a gas in reference and measurement paths of an interferometer.
One way to detect refractive index fluctuations is to measure changes in pressure and temperature along a measurement path and calculate the effect on the optical path length of the measurement path. Mathematical equations for effecting this calculation are disclosed in an article entitled “The Refractivity Of Air,” by F. E. Jones, J. Res. NBS 86(1), p 27 (1981). An implementation of the technique is described in an article entitled “High-Accuracy Displacement Interferometry In Air,” by W. T. Estler, Appl. Opt. 24(6), p 808 (1985). This technique provides approximate values, is cumbersome, and corrects for slow, global fluctuations in air density.
Another, more direct way to detect the effects of a fluctuating refractive index over a reference and/or measurement path is by multiple-wavelength distance measurement. The basic principle may be understood as follows. Interferometers and laser radar measure the optical path length between a reference and an object, most often in open air. The optical path length is the integrated product of the refractive index and the physical path traversed by a beam. In that the refractive index varies with wavelength, but the physical path is independent of wavelength, it is generally possible to determine the physical path length from the optical path length, particularly the contributions of fluctuations in refractive index, provided that the instrument employs at least two wavelengths. The variation of refractive index with wavelength is known in the art as dispersion and this technique is often referred to as the dispersion technique.
An example of a two-wavelength distance measurement system is described in an article by Y. Zhu, H. Matsumoto, T. O'ishi, SPIE 1319, Optics in Complex Systems, p 538 (1990), entitled “Long-Arm Two-Color Interferometer For Measuring The Change Of Air Refractive Index.” The system of Zhu et al. employs a 1064 nm wavelength YAG laser and a 632 nm HeNe laser together with quadrature phase detection. The interferometer of Zhu et al. has insufficient resolution for applications that require sub-micron displacement interferometry.
An example of a two wavelength high-precision interferometry system for microlithography is represented by U.S. Pat. No. 4,948,254 issued to A. Ishida (1990). A similar device is described by Ishida in an article entitled “Two Wavelength Displacement-Measuring Interferometer Using Second-Harmonic Light To Eliminate Air-Turbulence-Induced Errors,” Jpn. J. Appl. Phys. 28(3), L473-475 (1989). In the article, a displacement-measuring interferometer is disclosed which eliminates errors caused by fluctuations in the refractive index by means of two-wavelength dispersion detection. However, the motion of the object results in rapid variations in phase that make it difficult to detect accurately the effects of fluctuations in the refractive index.
In U.S. Pat. No. 5,404,222 entitled “Interferometric Measuring System With Air Turbulence Compensation,” by S. A. Lis, there is disclosed a two-wavelength interferometer employing the dispersion technique for detecting and compensating refractive index fluctuations. The principal innovation of this system with respect to that taught by Ishida in Jpn. J. Appl. Phys. (cited above) is the addition of a second BBO doubling crystal to improve the precision of the phase detection means. The additional BBO crystal makes it possible to optically interfere two beams having wavelengths that are exactly a factor of two different. The resultant interference has a phase that is directly dependent on the refractive index but is substantially independent of stage motion.
The application of multiple wavelength high-precision interferometric techniques to a single axis interferometer introduces considerable complexity and cost. In an application of multiple wavelength high-precision interferometric techniques to wavefront sensors, the considerable complexity and cost is compounded many fold wherein an application of the dispersion interferometric techniques is required for reference and measurement beam paths corresponding to each pixel of a large array of respective detector pixels to compensate for effects of atmospheric turbulence.
In U.S. Pat. No. 5,764,362 entitled “Superheterodyne Method And Apparatus For Measuring The Refractive Index Of Air Using Multiple-Pass Interferometry” by Henry A. Hill and P. de Groot and U.S. Pat. No. 5,838,485 entitled “Superheterodyne Interferometer And Methods For Compensating The Refractive Index Of Air Using Electronic Frequency Multiplication” by Peter de Groot and Henry A. Hill, there are described two two-wavelength distance measuring systems based on superheterodyne techniques. The first of the two cited patents is based on multiple pass interferometry and the second cited patent is based on electronic frequency multiplication. The application of the non-dispersive techniques described in U.S. Pat. Nos. 5,764,362 and 5,838,485 would require complex interferometric optical configurations and/or electronic signal processing for reference and measurement beam paths corresponding to each pixel of a large array of detector pixels of a wavefront sensor.
A non-dispersive apparatus and method for the compensation of atmospheric turbulent effects experienced by linear displacement interferometer is described in U.S. Pat. No. 6,839,141 B2 entitled “Method and Apparatus For Compensation Of Time-varying Optical Properties of Gas In Interferometry” by Henry A. Hill. U.S. Pat. No. 6,839,141 B2 compensates for turbulent effects of the gas on a first beam by using measured effects of the atmospheric turbulence on the directions of propagation of the first beam and a second beam. The application of the non-dispersive technique described in U.S. Pat. No. 6,839,141 B2 to wavefront interferometry would require that angle interferometers be added for the reference and measurement beam paths corresponding to each pixel of a large array of detector pixels of the respective wavefront sensor.
Another non-dispersive apparatus and method for the compensation of turbulent effects of a gas in a linear displacement interferometer is described in U.S. patent application Ser. No. 10/701,759 (Publication No. 20040141185 A1) entitled “Compensation of Refractivity Perturbations In An Interferometer Path” by Henry A. Hill. U.S. patent application Ser. No. 10/701,759 compensates for turbulent effects of the gas on the optical path length of a beam of an interferometer system by using measured transverse differential effects of the atmospheric turbulence at a single wavelength on the relative measurement path lengths of spatially separated first and second beams wherein cells of the gas that pass through the measurement path of the first beam are subsequently transported through the measurement path of the second beam. The transverse differential effects correspond to the difference between two electrical interference signal values from two linear displacement interferometers, respectively, wherein the two electrical interference signal values are obtained simultaneously. The interferometer system also comprises an angle interferometer to monitor changes in orientation of the measurement object in order to compensate for effects of orientation changes in the determination of effects of atmospheric effects on the beam of the interferometer system. The interferometer system further must acquire the surface figure of a measurement object from a different source when the measurement object is scanned during the use of the interferometer system, e.g., a stage mirror of a lithographic tool, in order to correct for effects departures of the measurement object from an assumed figure in the determination of the measured transverse differential effects.
Information about of effects of atmospheric turbulence are obtained in U.S. patent application Ser. No. 10/701,759 by the examination of measured transverse differential effects as a function of time, compensation for effects of changes in orientation of the measurement object, and subsequent summation or integration with respect to time of the transverse differential effects compensated for the effects of changes in orientation of the measurement object. The time period required for measuring and summing or integration with respect to time of the transverse differential effects compensated for effects of changes in orientation of the measurement object must be long compared to a characteristic time for changes of effects of atmospheric turbulence in order to achieve a statistically significant reduction of effects of atmospheric turbulence, e.g., the time period can be of the order of a second or longer. In applications such as to stage position metrology systems of lithographic tools where the respective stage mirror positions are monitored continuously, the long time period will generally not affect the throughput of the lithographic tool. However, in an application to wavefront interferometry where continuous monitoring of the respective measurement object is not typically part of a procedure for testing a measurement object surface, the required the time period may lead to a reduction of throughput. Also as a consequence of a property noted in the preceding paragraph, an application of U.S. patent application Ser. No. 10/701,759 to wavefront interferometry will encounter a difficult inverse problem: the wavefront for which information is being sought must be known prior to determination of the information in order to compensate for atmospheric turbulence effects while compensation for atmospheric turbulence effects must be performed in order to obtain the wavefront information.
The statistical accuracy to which the effects of atmospheric turbulence are determined in U.S. patent application Ser. No. 10/701,759 is directly related to the length of the time period and to information about atmospheric turbulence effects obtained from two column densities of gas corresponding to the reference and measurement beam paths of the first and second beams.
It is evident from the preceding material that a non-dispersive technique for the compensation of atmospheric turbulence effects in wavefront interferometry with improved statistical accuracy and which does not introduce complexities of dispersive techniques of prior art would be beneficial. It is further evident that it would be beneficial if the non-dispersive technique would meet these conditions with respect to complexity without the requirement of additional measurements or substantial additional measurements beyond that required for generating a measured array of conjugated quadratures representing a relative wavefront measurement, i.e. did not require additional time or substantial time beyond that required to obtain an array of conjugated quadratures representing a relative wavefront measurement.